 # A traveling wave along the x-axis is given by the following wave funct fanyattehedzg 2021-12-16 Answered
A traveling wave along the x-axis is given by the following wave function
$\psi \left(x,t\right)=4.8\mathrm{cos}\left(1.2x-8.2t+0.54\right)$, where x in meter, t in seconds, and ψ in meters. Read off the appropriate quantities for this wave function and find the following characteristics of this plane wave.
What is the frequency in Hertz, the wavelength in meters, the wave speed in meters per second, and the phase constant in radians
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Step 1
Given :
wave function, $\varphi \left(x,t\right)=4.8\mathrm{cos}\left(1.2x-8.2t+0.54\right)$ .....(1)
We have , general form of wave function,
$\varphi \left(x,t\right)=A\mathrm{cos}\left(kx-\omega t+\varphi \right)$ ............(2)
comparing (1) and (2) , we get,
$A=4.8$
$k=1.2$
$\omega =8.2$
$\varphi =0.54$
Step 2
- Frequency, $v=\frac{\omega }{2\pi }$
$v=\frac{8.2}{2\cdot \pi }$
$v=0.023Hz$
Therefore, frequency is 0.023 Hz.
Wave length, $\lambda =\frac{2\pi }{k}$
$\lambda =\frac{2\pi }{1.2}$
$\lambda =300m$
Therefore, wavelength is 300 m.
Step 3
Wave speed, $V=\nu \lambda$
$V=0.023\cdot 300$
$V=6.9\frac{m}{s}$
Therefore, wave speed is 6.9 m/s.
Phase constant, $\varphi =0.54$ radians

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